ON A GEOMETRIC PROPERTY OF POSITIVE DEFINITE MATRICES CONE

被引：2

作者：

Ito, Masatoshi ^{[2
]}

Seo, Yuki ^{[3
]}

Yamazaki, Takeaki ^{[1
]}

Yanagida, Masahiro ^{[4
]}

机构：

[1] Kanagawa Univ, Dept Math, Yokohama, Kanagawa 2218686, Japan

[2] Maebashi Inst Technol, Dept Integrated Design Engn, Maebashi, Gunma 3710816, Japan

[3] Shibaura Inst Technol, Fac Engn, Saitama 3378570, Japan

[4] Tokyo Univ Sci, Fac Sci, Dept Math Informat Sci, Tokyo 1628601, Japan

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2009年 / 3卷 / 02期

关键词：

Positive matrix; Riemannian metric; geometric mean;

D O I：

10.15352/bjma/1261086710

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We shall discuss the matrix geometric mean for the positive definite matrices. The set of all n x n matrices with a suitable inner product will be a Hilbert space, and the matrix geometric mean can be considered as a path between two positive matrices. In this paper, we shall obtain a matrix geometric mean inequality, and as an application of it, a property of Riemannian metric space is given. We also obtain some examples related to our result.

引用

页码：64 / 76

页数：13

共 50 条

[1] Geometric properties of positive definite matrices cone with respect to the Thompson metric
Ito, Masatoshi
Seo, Yuki
Yamazaki, Takeaki
Yanagida, Masahiro
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 435 (08) : 2054 - 2064
[2] A new positive definite geometric mean of two positive definite matrices
Fiedler, M
Ptak, V
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 251 : 1 - 20
[3] The geometric mean and B-loop quasigroups of the convex cone of positive definite matrices
Yongdo Lim
[J]. Archiv der Mathematik, 2005, 84 : 268 - 275
[4] The geometric mean and B-loop quasigroups of the convex cone of positive definite matrices
Lim, YD
[J]. ARCHIV DER MATHEMATIK, 2005, 84 (03) : 268 - 275
[5] Hamiltonian actions on the cone of positive definite matrices
Lim, Yongdo
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 460 : 1 - 16
[6] Factorizations and geometric means of positive definite matrices
Lim, Yongdo
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 437 (09) : 2159 - 2172
[7] ON PROJECTION OF A POSITIVE DEFINITE MATRIX ON A CONE OF NONNEGATIVE DEFINITE TOEPLITZ MATRICES
Filipiak, Katarzyna
Markiewicz, Augustyn
Mieldzioc, Adam
Sawikowska, Aneta
[J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2018, 33 : 74 - 82
[8] CONJUGATE CONE CHARACTERIZATION OF POSITIVE DEFINITE AND SEMIDEFINITE MATRICES
HAN, SP
MANGASARIAN, OL
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1984, 56 (JAN) : 89 - 103
[9] On the Surjectivity of Generalized Isometries on the Positive Definite Cone of Matrices
Molnar, Lajos
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2017, 14 (04)
[10] On the Surjectivity of Generalized Isometries on the Positive Definite Cone of Matrices
Lajos Molnár
[J]. Mediterranean Journal of Mathematics, 2017, 14

← 1 2 3 4 5 →